Problem: What do the following two equations represent? $3x+5y = -5$ $15x+25y = 2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x+5y = -5$ $5y = -3x-5$ $y = -\dfrac{3}{5}x - 1$ Putting the second equation in $y = mx + b$ form gives: $15x+25y = 2$ $25y = -15x+2$ $y = -\dfrac{3}{5}x + \dfrac{2}{25}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.